Bargaining When Only One Player Can Make Proposals

I consider a bargaining game in which, unlike the standard economic bargaining game (e.g. Rubenstein, 1982), only one player can make proposals. I also assume that the space of proposals is finite. Thus, the game is akin to (i) a CEO's proposing a hire who must be okayed by a board of directors, or (ii) the U.S. president's proposing a judge or cabinet member, who must be okayed by the Senate. I derive an algorithm that finds the unique subgame-perfect equilibrium to the game. As the algorithm reveals, a surprising aspect of the game is that only the wait costs of the non-proposer are relevant. The wait costs of the proposer are irrelevant. My review of the literature suggests that this result holds more generally: In bargaining games the patience of the proposer seems to be less important than the patience of the other players